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Dimensionality reduction (DR) is the key issue to improve the classifiers' efficiency for hyperspectral images (HSIs). In this paper, principal component analysis (PCA), independent component analysis, and projection pursuit (PP) approaches to DR have been investigated. These matrix-algebra methods are applied on vectorized images. Thereof, the spatial rearrangement is lost. To jointly take advantage of the spatial and spectral information, HSI has been recently represented as tensor. Offering multiple ways to decompose data orthogonally, we introduced DR methods based on multilinear-algebra tools. The DR is performed on spectral way using PCA, or PP, joint to an orthogonal projection onto a lower subspace dimension of the spatial ways. We show the classification improvement using the introduced methods in function to existing methods. This experiment is exemplified using real-world HYDICE data.